1. Field of the Invention
The present invention relates to an artificial satellite navigation system and method for determining the position of a spacecraft such as an artificial satellite (hereinafter generically an artificial satellite) using the global positioning system (GPS).
2. Description of the Related Art
A GPS receiver inversely decodes a GPS signal received from a GPS satellite according to a PRN code, one kind of pseudo random numbers, and then interprets a navigation message. Moreover, the GPS receiver locks the phase of a carrier on to that of a reference signal. A time difference between the instant a GPS signal is transmitted and the instant the GPS signal is received is multiplied by a the velocity of light, whereby the distance between the GPS satellite and receiver is measured. The distance is analyzed in conjunction with the position of the GPS satellite which is detected from the navigation message, thus determining the position of the receiver.
A clock included in a GPS receiver owned by a user is not always precise. When a time difference between transmission and reception is measured, a bias caused by the clock is added as an error. For locating a user independently, simultaneous equations including four unknown variables are solved using observed quantities that are distances from four GPS satellites. This method is generally adopted except when a user stays on the sea. In this case, it is apparent that the altitude is equal to the sea level. The four unknown variables include the bias caused by the receiver clock and three degrees of freedom concerning position, that is, latitude, longitude, and altitude. Furthermore, since the phase of a carrier is locked on to a reference signal, a change in distance from each GPS satellite is observed. For calculating velocity, simultaneous equations having four variables are solved using observed quantities that are changes in distance from the four GPS satellites. The four variables include a drift caused by the receiver clock and the three parameters concerning position. The principles of locating a user independently using the GPS have been described above.
However, a GPS signal contains a natural error such as a delay of a signal occurring during passage through the troposphere or ionosphere, and an artificial error that is applied intentionally for the purpose of national security; such as, an SA error. The precision in location ensured by the foregoing method is therefore unsatisfactory for some usage. A relative navigation method referred to as a differential GPS (hereinafter DGPS), which will be described below, has been proposed for locating an entity on the Earth in the past. The location precision has thus improved. The basic ideas of the DGPS are to detect the position and velocity of one receiver (user) relative to another receiver (reference station). Common errors occurring in the receivers are canceled out. Eventually, the location precision improves.
Referring to FIG. 7, the DGPS will be described. FIG. 7 is a block diagram showing the configuration of a navigation system based on the DGPS adaptable to the Earth. The configuration has been revealed in the article entitled "Guidance and Control in the Aerospace" written by Nishimura et al. (Association of Instrumentation and Automatic Control, pp.255-260, 1995). In FIG. 7, GPS satellites 1, 2, 3, and 4 are visible in common from both a reference station and user. A user 5 or a GPS receiver owned by the user 5 is shown. A communication unit 6 helps the user receive data such as quantities of correction from the reference station. Moreover, there are shown a reference station 7 or a GPS receiver installed in the reference station, and a communication unit 8 helping the reference station transmit data such as the quantities of correction to users. For brevity's sake, the GPS receiver shall include a GPS antenna.
The receiver 7 to be installed in the reference station is placed at a site whose position is accurately known. Data observed by the receiver is used to calculate quantities of correction that explicitly or implicitly contain common errors occurring in the user 5 and reference station 7. The quantities of correction are transmitted as DGPS correction data from the communication unit 8 to the user 5 through radio-communication or the like. The user 5 adds the quantities of correction received through the communication unit 6 to the results of location that are calculated based on the observed data, thus improving precision in location. The errors occurring in common in the receivers, for example, a delay caused by the ionosphere, an error caused by the troposphere, and an SA error can be canceled.
Since the reference station 7 is installed on the Earth, the position thereof is usually specified accurately according to a system of coordinates fitted to the Earth, for example, in terms of latitude, longitude, and altitude. Based on the quantities of correction, the position of the user 5 can be determined highly precisely according to the same system of coordinates fitted to the Earth. Otherwise, since the quantities of correction are used in common by the user and reference station, the relative positions thereof can be determined highly precisely in consideration of differences between the results of locating them. Quantities of correction to be calculated at the reference station 7 may include quantities proportional to biases of GPS signals or quantities proportional to biases of the results of location provided using an appropriate combination of GPS satellites. The former biases are referred to as differences detected in an observation field while the latter biases are referred to as differences detected in a navigation field.
When the differences detected in the observation region are employed, the quantities of correction vary depending on GPS satellites. After a signal is corrected for each GPS satellite, parameters needed for location are calculated. When the differences detected in the navigation field are employed, the quantities of correction vary depending on a combination of four GPS satellites used for location. The results of calculations for location are corrected. In either case, the number of common GPS satellites must be four or more. The reference station 7 to be installed on the Earth is usually positioned at a clear site. As long as the user 5 stays at a clear site not too far from the reference station 7, the number of GPS satellites visible in common by the user and reference station will be four. The number of GPS satellites required by the DGPS is thus satisfied.
Now, a space station in the space will be regarded as a reference station (hereinafter called a target). An artificial satellite taking off from or landing on the space station will be regarded as a user (hereinafter called a chaser). The relative position of the chaser with respect to the target can presumably be estimated highly precisely by the DGPS. However, the DGPS adaptable to the Earth cannot be adapted to the space for the reasons described below.
To begin with, the target has numerous large accessories including a solar paddle and a radiating plane. The field of view offered by a GPS antenna is liable to be blocked. Frequently three or fewer of the GPS satellites are visible in common by the target and chaser. Furthermore, both the target and chaser are moving at high speeds in space. For avoiding accidents including a collision, it is indispensable that the relative position or velocity of the chaser can be estimated any time. For this reason, the DGPS adaptable to the Earth and making it an indispensable requisite that four or more GPS satellites must be visible in common cannot be adapted to space.
A DGPS proposed for the space is described, for example, in "Guidance and Control in Aerospace" written by Nishimura et al. (Association of Instrumentation and Automatic Control, pp.273-275, 1995). Specifically, measurements are predicted based on a relative position and velocity predicted by integrating equations of motion that give the relative position of the chaser with respect to the target. The predicted values of the relative position and velocity are corrected according to the actual measurements (hereinafter, when it is stated that measurements are updated, it means that measurements are predicted and then corrected as mentioned above). In other words, the differences detected in the observation field are extended.
The Kalman filter composed of equations of motion and measurements is adopted as mentioned above. Even if the number of GPS satellites visible in common is less than four, measurements can be updated. When equations of motion giving a relative position are kept integrated, an error contained in an estimated value is integrated and expanded. Besides, measurements are affected by disturbances including air resistance and an aspherical component of the gravity of the Earth. The precision in measuring therefore deteriorates quickly with the passage of time. If four or more GPS satellites are visible in common, the precision in location will be improved by updating measurements. Even if the number of GPS satellites visible in common is less than four, deterioration of precision in location can be suppressed by updating measurements.
However, if the target is located very far from the chaser, no GPS satellite will be visible in common. The foregoing method cannot therefore be adopted for updating measurements. Moreover, biases and drifts caused by the clocks in the receivers of the chaser and target are a quantity estimated by the filter, that is, a state quantity provided by the filter. The characteristics of the receiver clock of the target causing bias and drift are not always known by the chaser. The filter is therefore tuned so that it can provide an estimated quantity large enough to compensate for the bias and drift. The filter cannot therefore be tuned optimally.
In the aforesaid conventional artificial satellite navigation system, even when the number of GPS satellites visible in common is less than four, differences are detected in an observation field so that measurements can be updated. A state quantity provided by a filler contains bias and drift caused by a clock included in a receiver of a target. The characteristics of the clock concerning the drift and bias are not always certain. This poses a problem in that the filter must be tuned so that the state quantity will be large enough to compensate for the drift and bias. Moreover, when no GPS satellite is visible in common, measurements cannot be updated. There arises a problem because the navigation system cannot be used to navigate an artificial satellite located far from the target.